The　functional　relations　between　the　modified　couple　stress　theory　(MCST)　and　the　classical　theory　(CT)　are　derived　and　analyzed　in　detail　for　closed-form　solutions　of　Timoshenko　micro-beam.　The　results　show　that　phenomenon　of　sharp　change　exists　in　the　internal　force　fields　at　two　ends　of　the　micro-beam.　This　phenomenon　is　related　to　dimensionless　material　scale　parameter　l/h.　The　phenomenon　at　fixed　end　is　different　from　that　at　free　end　because　the　shear　force　Q　at　fixed　end　cannot　be　degenerated　from　the　MCST　to　the　CT,　which　is　proved　from　a　mathematical　point　of　view.　What＇s　more,　the　exponential　functions　in　the　closed-form　solutions　of　the　MCST　are　higher-order　terms　and　can　be　ignored　for　the　deflection　and　rotation　when　Poisson＇s　ratio　nu　=　0-0.45,　h/L　=　1/100-1/8　and　the　l/h　=　0-1.　After　exponential　functions　are　omitted,　except　rotation　of　cantilever　beam　under　bending　moment　M-0,　the　concise　solutions　are　acquired　and　error　is　very　small.　The　size　effects　of　the　deflection　and　rotation　can　be　calculated　quickly　without　additional　computing　tools　by　the　concise　solutions.　Some　results　obtained　in　this　paper　are　compared　with　the　published　data　in　literatures,　which　prove　the　correctness　of　the　results　in　this　paper.